A New Pressure/Rate Deconvolution Algorithm to Analyze Wireline Formation Tester and Well-Test Data

Abstract

The deconvolved pressure change and its natural-logarithmic time (or Bourdet) derivative are very important for wellbore/reservoir system identification in pressure transient interpretation because they represent the constant-rate drawdown response of the system. In recent years, the use of pressure/rate deconvolution has increased considerably due to significant improvement of the mathematical algorithms. In this paper, we present a robust deconvolution algorithm based on a weighted Euclidean norm in the Tikhonov regularized objective function so that one can assign weights to individual pressure and rate measurement points, and thus define different error estimates for different sections of the data. Incorporating such features into the deconvolution algorithm is very useful to mitigate the effects of unreliable pressure and rate measurements and the sections of the data not obviously consistent with the wellbore/reservoir model. In the deconvolution algorithm, the Levenberg-Marquardt method with a restricted step procedure is used for the minimization of the objective function. We present several applications of the new algorithm using real field pressure/rate transient data sets. In addition to well test data, we apply the algorithm to wireline formation-tester pressure transients which are usually also referred to as Interval Pressure Transient Tests (IPTT). The examples include data with cleanup effects as well as an IPTT test, followed by a conventional Drill Stem Test (DST). To the best of our knowledge, applications of deconvolution to wireline formation-tester pressure transients have been limited to a single publication before. Hence, the deconvolution algorithm and the results in this paper will be useful in designing and interpreting wireline formation tester pressure transients in addition to pressure transient well tests.

Multiple Well Deconvolution

“…Identifying good choices for these hyperparameters is a challenging problem, and various methods have been proposed -see for example Cumming et al (2013), Levitan (2006), Pimonov et al (2009), von Schroeter et al (2004. In single-well deconvolution, the purpose of these hyperparameters is to balance the contributions of the four components of the error function in such a way that leads to good quality deconvolutions.…”

“…In contrast to von Schroeter et al (2004), we do not set R = 1 and adjust the remaining parameters to compensate as this make the variance estimation much more challenging and less robust. These weights can be easily generalized by vectorizing the scaling factors to act as weights for individual or ranges of data points as in Pimonov et al (2009), thus allowing the flexibility to emphasize good matches at particular wells or during particular times, e.g. build-ups.…”

3D Multiphase Streamline-Based Method for Interpretation of Formation-Tester Measurements Acquired in Vertical and Deviated Wells

“…Recent SL techniques developed for large-scale applications can include at least one injector and one producer well (Behrens et al, 1999;King et al, 1998;Kulkarni et al, 2001). In formation testing, injection or production sources are located in one single well (Pimonov et al, 2010;Seifert et al, 2005).…”

New Regularization Algorithms for Solving the Deconvolution Problem in Well Test Data Interpretation

“…In a subsequent paper by Levitan et al [21], valuable suggestions were made for practical applications of the pressure-rate deconvolution. Pimonov et al [22,23] further modified the deconvolution algorithm of von Schroeter et al [18,19] and Levitan [20]. The modification was done by introducing a more general objective function in the Levenberg-Marquardt minimization procedure.…”

“…The modification was done by introducing a more general objective function in the Levenberg-Marquardt minimization procedure. This algorithm was successfully applied by Pimonov et al [22,23] to deconvolution of drillstem test data and wireline formation tester data. Recently, a totally different approach for solving the nonlinear Equation (1) was proposed by Ageev et al [24], where the authors used an iteratively regularized modified Levenberg-Marquardt method.…”